2-level Toeplitz systems arise in many applications, image restoration, image processing, tomography, PDE's, e.t.c, thus an efficient strategy for their solution are often required. The already known methods require the explicit knowledge of the generating function f of the considered system An(f)x = b. This hypothesis is not usually fulfilled in real applications. In this paper we extend the technique proposed by S. Serra for unilevel Toeplitz systems, to multilevel Toeplitz systems. From the knowledge of the coefficients of An(f), we try to determine the best preconditioning strategy for the solution of the system. More precisely, we propose and analyze an algorithm that economically determine the minimal features of f allowing us to select the best iterative method. Various numerical experiments are stated which fully confirm the effectiveness of the proposed technique.
1 Joint work with Stefano SERRA CAPIZZANO and Paris VASSALOS.